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arXiv · 1802.01857

Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map

Georgi Vodev
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Abstract

We study the semi-classical microlocal structure of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We build a new, improved parametrix in the glancing region compaired with that one built in [9], [12]. We also study the way in which the parametrix depends on the refraction index. As a consequence, we improve the transmission eigenvalue-free regions obtained in [12] in the isotropic case when the restrictions of the refraction indices on the boundary coincide.

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Georgi Vodev. 2018-02-06. Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map. https://arxiv.org/abs/1802.01857

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